Contrastive explanations for images with monotonic attribute functions

ABSTRACT

In an embodiment, a method for generating contrastive information for a classifier prediction comprises receiving image data representative of an input image, using a deep learning classifier model to predict a first classification for the input image, evaluating the input image using a plurality of classifier functions corresponding to respective high-level features to identify one or more of the high-level features absent from the input image, and identifying, from among the high-level features absent from the input image, a pertinent-negative feature that, if added to the input image, will result in the deep learning classifier model predicting a second classification for the modified input image, the second classification being different from the first classification. In an embodiment, the method includes creating a pertinent-positive image that is a modified version of the input image that has the first classification and fewer than all superpixels of the input image.

TECHNICAL FIELD

The present invention relates generally to machine learning. Moreparticularly, the present invention relates to explaining deep learningsystems.

BACKGROUND

Artificial intelligence (AI) technology has evolved significantly overthe past few years. Modern AI systems are achieving human levelperformance on cognitive tasks like converting speech to text,recognizing objects and images, or translating between differentlanguages. This evolution holds promise for new and improvedapplications in many industries.

An Artificial Neural Network (ANN)—also referred to simply as a neuralnetwork—is a computing system made up of a number of simple, highlyinterconnected processing elements (nodes), which process information bytheir dynamic state response to external inputs. ANNs are processingdevices (algorithms and/or hardware) that are loosely modeled after theneuronal structure of the mammalian cerebral cortex but on much smallerscales. A large ANN might have hundreds or thousands of processor units,whereas a mammalian brain has billions of neurons with a correspondingincrease in magnitude of their overall interaction and emergentbehavior.

A Deep Learning Neural Network, referred to herein as a Deep NeuralNetwork (DNN) is an artificial neural network (ANN) with multiple hiddenlayers of units between the input and output layers. Similar to shallowANNs, DNNs can model complex non-linear relationships. DNNarchitectures, e.g., for object detection and parsing, generatecompositional models where the object is expressed as a layeredcomposition of image primitives. The extra layers enable composition offeatures from lower layers, giving the potential of modeling complexdata with fewer units than a similarly performing shallow network. DNNsare typically designed as feedforward networks.

SUMMARY

The illustrative embodiments provide a method, system, and computerprogram product for explaining machine learning models. In anembodiment, the method includes receiving, by one or more processors,image data representative of an input image, predicting, by one or moreprocessors, using a DNN classifier model, a first classification for theinput image, evaluating, by one or more processors, the input imageusing a plurality of classifier functions corresponding to respectivehigh-level features to identify one or more of the high-level featuresabsent from the input image, and identifying, by one or more processors,from among the high-level features absent from the input image, apertinent-negative feature that, if added to the input image, willresult in the DNN classifier model predicting a second classificationfor the modified input image, the second classification being differentfrom the first classification.

An embodiment includes a computer usable program product for generatingcontrastive information for a classifier prediction, the computer usableprogram product comprising a computer-readable storage device, andprogram instructions stored on the storage device, the stored programinstructions comprising program instructions to receive, by one or moreprocessors, image data representative of an input image, programinstructions to predict, by one or more processors, using a DNNclassifier model, a first classification for the input image, programinstructions to evaluate, by one or more processors, the input imageusing a plurality of classifier functions corresponding to respectivehigh-level features to identify one or more of the high-level featuresabsent from the input image, and program instructions to identify, byone or more processors, from among the high-level features absent fromthe input image, a pertinent-negative feature that, if added to theinput image, will result in the DNN classifier model predicting a secondclassification for the modified input image, the second classificationbeing different from the first classification. In an embodiment, themethod includes creating a pertinent-positive image that is a modifiedversion of the input image that has the first classification and fewerthan all superpixels of the input image.

In an embodiment, a computer system comprising a processor, acomputer-readable memory, and a computer-readable storage device, andprogram instructions stored on the storage device for execution by theprocessor via the memory, the stored program instructions comprisingprogram instructions to receive, by one or more processors, image datarepresentative of an input image, program instructions to predict, byone or more processors, using a DNN classifier model, a firstclassification for the input image, program instructions to evaluate, byone or more processors, the input image using a plurality of classifierfunctions corresponding to respective high-level features to identifyone or more of the high-level features absent from the input image, andprogram instructions to identify, by one or more processors, from amongthe high-level features absent from the input image, apertinent-negative feature that, if added to the input image, willresult in the DNN classifier model predicting a second classificationfor the modified input image, the second classification being differentfrom the first classification.

BRIEF DESCRIPTION OF THE DRAWINGS

The novel features believed characteristic of the invention are setforth in the appended claims. The invention itself, however, as well asa preferred mode of use, further objectives and advantages thereof, willbest be understood by reference to the following detailed description ofthe illustrative embodiments when read in conjunction with theaccompanying drawings, wherein:

FIG. 1 depicts a block diagram of a network of data processing systemsin which illustrative embodiments may be implemented;

FIG. 2 depicts a block diagram of a data processing system in whichillustrative embodiments may be implemented;

FIG. 3 depicts a block diagram of an example configuration for providingan artificial intelligence prediction of a classification of an imagealong with contrastive explanations for the prediction;

FIG. 4 depicts a flowchart of an example process for classifying datausing machine learning that generates contrastive explanations inaccordance with an illustrative embodiment;

FIG. 5 depicts a block diagram of an exemplary output report from aprocess for classifying data using machine learning that generatescontrastive explanations in accordance with an illustrative embodiment;

FIG. 6 depicts a flowchart of an example process for creating aPertinent Negative image in accordance with an illustrative embodiment;and

FIG. 7 depicts a flowchart of an example process for creating aPertinent Positive image in accordance with an illustrative embodiment.

DETAILED DESCRIPTION

In recent years, DNNs have demonstrated the ability to make remarkablyaccurate predictions and have emerged as the state-of-the-art in machinelearning models. DNNs now outperform other methods in several areas,including applications involving image recognition, such as computervision and image classification. This translates to tremendous potentialfor the use of DNNs in many different industries, including the medicaland transportation industries. For example, DNNs show promise forapplications such as medical imaging and self-driving vehicles. However,the benefit DNNs bring is currently seen as coming with some amount ofrisk due to the difficulty involved in understanding how exactly DNNsarrive at their predictions. This is sometimes referred to as the “blackbox” problem of DNNs: while they consistently demonstrate amazingaccuracy, there remains a degree of mistrust because the predictions arebased on a process that is not readily understood. For example, in themedical industry, DNNs have outperformed human counterparts atevaluating medical imagery or developing care plans based on lengthypatient records. However, the illustrative embodiments recognize that ifa physician reviewing the DNN's prediction has no way of understandingthe reasoning that led to the conclusion, it becomes difficult for thephysician to decide how much confidence to place on the DNN'sprediction. Thus, the illustrative embodiments recognize that mistrustdue to an absence of explanation for a DNNs prediction presents anobstacle to adoption of DNNs particularly in areas like medical andtransportation applications where health and safety are put at risk ifpredictions are wrong.

The illustrative embodiments recognize that there is a need to improvethe transparency of Deep Neural Network (DNN) decision-making byproviding humanly-interpretable explanations of predictions made byDNNs. For example, a physician reviewing a prediction made by a DNN ofwhether a medical image indicates a medical condition has only theinscrutable prediction of the DNN and therefore cannot be certainwhether it was a close call or which areas of the image most contributedto the DNN's prediction. Without the ability to understand the rationalebehind the DNN's prediction, the physician's decision-making abilitymight be hampered or adversely altered. For example, the physician mightordinarily err on the side of caution and treat a close negative result,but fail to do so when not aware of the close, and therefore potentiallyerroneous, nature of a prediction made by the DNN.

Understanding why a DNN made one particular prediction instead ofanother is also important in developing future machine learning models.For example, a DNN classifier that is making erroneous predictions canbe difficult to troubleshoot with only the erroneous inscrutableprediction. In a case where the errors stem from an adversarial attackon the DNN, the rationale for the erroneous decision might aid in betterunderstanding the nature of the adversarial attack and how to defendfrom such an attack in the future.

In addition, DNNs have the potential to improve many different securityapplications, such as at airports or other secure areas. For example, aDNNs have shown potential for security applications such as facialrecognition, retina scanning, and biometric scanning. Securityapplications such as these present challenges due to the potentialthreat of adversarial attacks or other attempts to bypass security bycausing the DNN to make erroneous predictions. The rationale of the DNNthat is contributing to the erroneous predictions can help improve therobustness of such systems to make such attacks more difficult.

The illustrative embodiments recognize that the presently availabletools or solutions do not address these needs or provide adequatesolutions for these needs. The illustrative embodiments used to describethe invention generally address and solve the above-described problemsand other problems related to improving the transparency of DNNdecision-making by providing humanly-interpretable explanations ofpredictions made by DNNs.

An embodiment can be implemented as a software application. Theapplication implementing an embodiment can be configured as amodification of an existing image analysis system, as a separateapplication that operates in conjunction with an existing image analysissystem, a standalone application, or some combination thereof.

Particularly, some illustrative embodiments provide a method thatutilizes a DNN classifier to classify an original image, and thengenerates an altered version of the original image that includes atleast one high-level feature that serves as a humanly-interpretablecontrastive explanation for the DNN's classification of the originalimage. In some such embodiments, the altered version of the originalimage is a “Pertinent Negative” (or “PN”) image that ishumanly-interpretable, from which nothing has been removed (i.e., noportion of the original image has been removed), and in which at leastone high-level feature (that is also humanly-interpretable) has beenadded that results in both a relatively small change to the originalimage and a different classification prediction by the DNN classifier.

A distinction between two classifications of images is now made forpurposes of clarity. A first classification of images are those that aremachine recognizable at any level of detail, whereas a secondclassification of images are those that are recognizable to the typicalhuman eye without the aid of a machine. A microscopic image that is toosmall to be discerned by an unaided human eye, but can be seen with thehelp of a microscope, is an example of the first classification ofimages. An image that can serve as a humanly-interpretable explanationis an example of the second classification of images because ahumanly-interpretable explanation in the form of a digital image is avisible image, meaning that it is large enough that a typical unaidedhuman eye can discern the image without the aid of a machine.Hereinafter, any reference to humanly recognizable, or humanlyinterpretable, or humanly readable, and other human-ability relatedterms refer to such operations or actions relative to artifacts fallingin the second classification. The term “high-level feature,” as usedherein, generally refers to depictions in the second classification ofimages, and are thus humanly-detectable images or depictions of objectsin an image, such as humanly-recognizable shapes or items. Imagesinclude two types of features: “high-level features” and “low-levelfeatures.” Low-level features are the fine details of an image, such asline segments or dots. Low-level features sometimes serve as buildingblocks for high-level features. High-level features in an image can bedetected by a DNN. Low level features in an image, such as lines ordots, can be detected by a convolutional filter, a Histogram of OrientedGradients (HOG), or a Scale Invariant Feature Transform (SIFT). A HOGbreaks patches up in blocks, and then constructs histograms representinggradient in the block. A SIFT transforms an image into a largecollection of local-feature vectors (local descriptors called SIFTkeys), and is sometimes is used for feature transformation of image.

For example, in some embodiments, a DNN includes multiple layers betweenthe input and output ports. In such embodiments, the architecture of aDNN is arranged such that different layers detect patterns withdifferent scales of granularity. For example, in some embodiments, on alow level, this includes detecting low-level features, such as specificpixel patterns, for example corners, lines, or dots. On a high level,this includes detecting high-level features such as detecting ofpatterns, faces, or graphical indicia (e.g., text, logos, or emoticons),like that a person is detected in the image or that a message expresseshappiness.

For an alternative basis for understanding the DNN classifier'srationale, some embodiments provide a method that utilizes a DNNclassifier to classify an original image, and then generates an alteredversion of the original image to which nothing has been added but fromwhich areas have been removed. The portion of the original image thatremains is indicative of one or more areas of the original image thatthe DNN treated as significant in predicting a classification of theoriginal image. In some such embodiments, the altered image is a“Pertinent Positive” (or “PP”) image that is humanly-interpretable,which is an altered version of the original image to which nothing hasbeen added, and from which regions of the image have been removed suchthat the remaining regions represent features (that are alsohumanly-interpretable) that are minimally sufficient for the DNNclassifier to continue to predict the same classification as that of theoriginal image.

Still further embodiments allow for an understanding of the DNNclassifier's rationale that is based on more than onehumanly-interpretable contrastive explanation. For example, someembodiments provide a method that utilizes a DNN classifier to classifyan original image, and then generates a humanly-interpretable PN image,which is an altered version of the original image from which nothing hasbeen removed and in which at least one high-level feature (that is alsohumanly-interpretable) has been added that results in both a relativelysmall change to the original image and a different classificationprediction by the DNN classifier, and also generates ahumanly-interpretable PP image, which is an altered version of theoriginal image to which nothing has been added, and from which regionsof the image have been removed such that the remaining regions representfeatures (that are also humanly-interpretable) that are minimallysufficient for the DNN classifier to continue to predict the sameclassification as that of the original image.

The term “contrastive explanation,” as used herein, generally refers toan explanation that describes why a decision was made by describing adifference in circumstances that would result in a different decision.For example, in some embodiments, a contrastive explanation for a DNNprediction includes a PN, which is a high-level feature that, when addedto an original image, alters the original image less than when certainother high-level features are added and causes the DNN classifier topredict a classification for the altered image that differs from that ofthe original image. As another example, in some embodiments, acontrastive explanation for a DNN prediction includes a PP, whichgenerally refers to one or more areas of an original image that areindicative of what the DNN classifier considers to be is minimallysufficient to justify the classifier's predicted classification for theoriginal image, e.g., the parts (e.g., minimal pixels) that keep animage in its current class when evaluated by a particular classifier.

An embodiment configures an image classification model to classify asubject viewed or captured by an image capturing device, which can beany device capable of generating a digital image, such as a camera,x-ray scanner, Magnetic resonance imaging (MRI) scanner, or computerizedtomography (CT) scanner. The subject may be viewed in real time orcaptured and viewed at a later time. In one embodiment, the imageclassification model is a DNN. During the configuration process, anembodiment uses labelled images of various subjects to train the neuralnetwork-based model to classify a subject of an image according to thetraining. For example, an image classification model that is intended toclassify an image subject as either a human face or something other thana human face could be trained using a set of images labelled asincluding a human face and another set of images labelled as notincluding a human face. As another example, an image classificationmodel that is intended to classify an image subject into one of a set ofknown household objects (e.g. chairs, books, tables, televisions, remotecontrols, sofas, etc.) could be trained using a set of images labelledas including a particular known household object and another set ofimages labelled as not including a particular known household object.

An embodiment provides a method that utilizes a DNN classifier toclassify an original image, and then generates a humanly-interpretablePN image, which is an altered version of the original image from whichnothing has been removed and in which at least one high-level feature(that is also humanly-interpretable) has been added that results in botha relatively small change to the original image and a differentclassification prediction by the DNN classifier.

Other image classification models and depth classification models, bothneural network-based and not utilizing a neural network, are alsopossible and contemplated within the scope of the illustrativeembodiments. Other configuration methods for each model, usingunsupervised learning or using a set of learned or static rules, arealso possible and contemplated within the scope of the illustrativeembodiments. In addition, one embodiment can implement modelconfiguration as a one-time process, and another embodiment canimplement model configuration on an ongoing basis, allowing additionalmodel refinement as an embodiment is used to classify an object in ascene.

Some embodiments configure the classifier models using one system, thenexecute the configured models using a different system, and generate acontrastive explanation using yet another system. Such embodimentsprovide for systems to be tailored or chosen based on a narrower rangeof tasks, allowing for more efficient use of resources. Such embodimentsalso allow for parallel performance of certain tasks, such as generatingthe PN and PP simultaneously or during time frames that overlap forapplicable embodiments. Alternatively, in some embodiments, a singlesystem can be used to perform the whole process.

In some embodiments, a specialized apparatus that includes an imagecapturing device for generating an original image is further configuredto execute at least some of the other tasks disclosed herein. Forexample, a CT scanner combines a series of X-ray images taken fromdifferent angles around a body and uses computer processing to createcross-sectional images (slices) of the bones, blood vessels and softtissues inside your body. Some embodiments can include a CT scannerhaving computer processing system integrated therewith or incommunication therewith that is configured to perform at least some ofthe tasks disclosed herein. Other examples of specialized equipment thatcan be include at least some of the functionality described hereininclude other medical equipment, for example MRI scanners, or securityequipment, for example security screening systems or security cameras.

For the sake of clarity of the description, and without implying anylimitation thereto, the illustrative embodiments are described usingsome example configurations. From this disclosure, those of ordinaryskill in the art will be able to conceive many alterations, adaptations,and modifications of a described configuration for achieving a describedpurpose, and the same are contemplated within the scope of theillustrative embodiments.

Furthermore, simplified diagrams of the data processing environments areused in the figures and the illustrative embodiments. In an actualcomputing environment, additional structures or component that are notshown or described herein, or structures or components different fromthose shown but for a similar function as described herein may bepresent without departing the scope of the illustrative embodiments.

Furthermore, the illustrative embodiments are described with respect tospecific actual or hypothetical components only as examples. The stepsdescribed by the various illustrative embodiments can be adapted forproviding explanations for decisions made by a machine-learningclassifier model, for example

Any specific manifestations of these and other similar artifacts are notintended to be limiting to the invention. Any suitable manifestation ofthese and other similar artifacts can be selected within the scope ofthe illustrative embodiments.

The examples in this disclosure are used only for the clarity of thedescription and are not limiting to the illustrative embodiments. Anyadvantages listed herein are only examples and are not intended to belimiting to the illustrative embodiments. Additional or differentadvantages may be realized by specific illustrative embodiments.Furthermore, a particular illustrative embodiment may have some, all, ornone of the advantages listed above.

Furthermore, the illustrative embodiments may be implemented withrespect to any type of data, data source, or access to a data sourceover a data network. Any type of data storage device may provide thedata to an embodiment of the invention, either locally at a dataprocessing system or over a data network, within the scope of theinvention. Where an embodiment is described using a mobile device, anytype of data storage device suitable for use with the mobile device mayprovide the data to such embodiment, either locally at the mobile deviceor over a data network, within the scope of the illustrativeembodiments.

The illustrative embodiments are described using specific code,contrastive explanations, computer readable storage medium, high-levelfeatures, historical data, designs, architectures, protocols, layouts,schematics, and tools only as examples and are not limiting to theillustrative embodiments. Furthermore, the illustrative embodiments aredescribed in some instances using particular software, tools, and dataprocessing environments only as an example for the clarity of thedescription. The illustrative embodiments may be used in conjunctionwith other comparable or similarly purposed structures, systems,applications, or architectures. For example, other comparable mobiledevices, structures, systems, applications, or architectures therefor,may be used in conjunction with such embodiment of the invention withinthe scope of the invention. An illustrative embodiment may beimplemented in hardware, software, or a combination thereof.

The examples in this disclosure are used only for the clarity of thedescription and are not limiting to the illustrative embodiments.Additional data, operations, actions, tasks, activities, andmanipulations will be conceivable from this disclosure and the same arecontemplated within the scope of the illustrative embodiments.

Any advantages listed herein are only examples and are not intended tobe limiting to the illustrative embodiments. Additional or differentadvantages may be realized by specific illustrative embodiments.Furthermore, a particular illustrative embodiment may have some, all, ornone of the advantages listed above.

With reference to the figures and in particular with reference to FIGS.1 and 2, these figures are example diagrams of data processingenvironments in which illustrative embodiments may be implemented. FIGS.1 and 2 are only examples and are not intended to assert or imply anylimitation with regard to the environments in which differentembodiments may be implemented. A particular implementation may makemany modifications to the depicted environments based on the followingdescription.

FIG. 1 depicts a block diagram of a network of data processing systemsin which illustrative embodiments may be implemented. Data processingenvironment 100 is a network of computers in which the illustrativeembodiments may be implemented. Data processing environment 100 includesnetwork 102. Network 102 is the medium used to provide communicationslinks between various devices and computers connected together withindata processing environment 100. Network 102 may include connections,such as wire, wireless communication links, or fiber optic cables.

Clients or servers are only example roles of certain data processingsystems connected to network 102 and are not intended to exclude otherconfigurations or roles for these data processing systems. Dataprocessing system 104 couples to network 102. Software applications mayexecute on any data processing system in data processing environment100. Any software application described as executing in processingsystem 104 in FIG. 1 can be configured to execute in another dataprocessing system in a similar manner. Any data or information stored orproduced in data processing system 104 in FIG. 1 can be configured to bestored or produced in another data processing system in a similarmanner. A data processing system, such as data processing system 104,may contain data and may have software applications or software toolsexecuting computing processes thereon. In an embodiment, data processingsystem 104 includes memory 124, which includes application 105A that maybe configured to implement one or more of the data processor functionsdescribed herein in accordance with one or more embodiments.

Server 106 couples to network 102 along with storage unit 108. Storageunit 108 includes a database 109 configured to store data as describedherein with respect to various embodiments, for example image data andattribute data. Server 106 is a conventional data processing system. Inan embodiment, server 106 includes neural network application 105B thatmay be configured to implement one or more of the processor functionsdescribed herein in accordance with one or more embodiments.

Clients 110, 112, and 114 are also coupled to network 102. Aconventional data processing system, such as server 106, or client 110,112, or 114 may contain data and may have software applications orsoftware tools executing conventional computing processes thereon.

Only as an example, and without implying any limitation to sucharchitecture, FIG. 1 depicts certain components that are usable in anexample implementation of an embodiment. For example, server 106, andclients 110, 112, 114, are depicted as servers and clients only asexample and not to imply a limitation to a client-server architecture.As another example, an embodiment can be distributed across several dataprocessing systems, and a data network as shown, whereas anotherembodiment can be implemented on a single data processing system withinthe scope of the illustrative embodiments. Conventional data processingsystems 106, 110, 112, and 114 also represent example nodes in acluster, partitions, and other configurations suitable for implementingan embodiment.

Device 132 is an example of a conventional computing device describedherein. For example, device 132 can take the form of a smartphone, atablet computer, a laptop computer, client 110 in a stationary or aportable form, a wearable computing device, or any other suitabledevice. In an embodiment, device 132 sends requests to server 106 toperform one or more data processing tasks by neural network application105B such as initiating processes described herein of the neuralnetwork. Any software application described as executing in anotherconventional data processing system in FIG. 1 can be configured toexecute in device 132 in a similar manner. Any data or informationstored or produced in another conventional data processing system inFIG. 1 can be configured to be stored or produced in device 132 in asimilar manner.

Server 106, storage unit 108, data processing system 104, and clients110, 112, and 114, and device 132 may couple to network 102 using wiredconnections, wireless communication protocols, or other suitable dataconnectivity. Clients 110, 112, and 114 may be, for example, personalcomputers or network computers.

In the depicted example, server 106 may provide data, such as bootfiles, operating system images, and applications to clients 110, 112,and 114. Clients 110, 112, and 114 may be clients to server 106 in thisexample. Clients 110, 112, 114, or some combination thereof, may includetheir own data, boot files, operating system images, and applications.Data processing environment 100 may include additional servers, clients,and other devices that are not shown.

In the depicted example, memory 124 may provide data, such as bootfiles, operating system images, and applications to processor 122.Processor 122 may include its own data, boot files, operating systemimages, and applications. Data processing environment 100 may includeadditional memories, processors, and other devices that are not shown.

In an embodiment, one or more of neural network application 105A of dataprocessing system 104 and neural network application 105B of server 106implements an embodiment of a neural network, such as a DNN, asdescribed herein. In a particular embodiment, the neural network isimplemented using one of network application 105A and networkapplication 105B within a single server or processing system. In anotherparticular embodiment, the neural network is implemented using bothnetwork application 105A and network application 105B within a singleserver or processing system. Server 106 includes multiple GPUs 107including multiple nodes in which each node may include one or more GPUsas described herein.

In the depicted example, data processing environment 100 may be theInternet. Network 102 may represent a collection of networks andgateways that use the Transmission Control Protocol/Internet Protocol(TCP/IP) and other protocols to communicate with one another. At theheart of the Internet is a backbone of data communication links betweenmajor nodes or host computers, including thousands of commercial,governmental, educational, and other computer systems that route dataand messages. Of course, data processing environment 100 also may beimplemented as a number of different types of networks, such as forexample, an intranet, a local area network (LAN), or a wide area network(WAN). FIG. 1 is intended as an example, and not as an architecturallimitation for the different illustrative embodiments.

Among other uses, data processing environment 100 may be used forimplementing a client-server environment in which the illustrativeembodiments may be implemented. A client-server environment enablessoftware applications and data to be distributed across a network suchthat an application functions by using the interactivity between aconventional client data processing system and a conventional serverdata processing system. Data processing environment 100 may also employa service-oriented architecture where interoperable software componentsdistributed across a network may be packaged together as coherentbusiness applications. Data processing environment 100 may also take theform of a cloud, and employ a cloud computing model of service deliveryfor enabling convenient, on-demand network access to a shared pool ofconfigurable computing resources (e.g. networks, network bandwidth,servers, processing, memory, storage, applications, virtual machines,and services) that can be rapidly provisioned and released with minimalmanagement effort or interaction with a provider of the service.

With reference to FIG. 2, this figure depicts a block diagram of a dataprocessing system in which illustrative embodiments may be implemented.Data processing system 200 is an example of a conventional computer,such as data processing system 104, server 106, or clients 110, 112, and114 in FIG. 1, or another type of device in which computer usableprogram code or instructions implementing the processes may be locatedfor the illustrative embodiments.

Data processing system 200 is also representative of a conventional dataprocessing system or a configuration therein, such as conventional dataprocessing system 132 in FIG. 1 in which computer usable program code orinstructions implementing the processes of the illustrative embodimentsmay be located. Data processing system 200 is described as a computeronly as an example, without being limited thereto.

Implementations in the form of other devices, such as device 132 in FIG.1, may modify data processing system 200, such as by adding a touchinterface, and even eliminate certain depicted components from dataprocessing system 200 without departing from the general description ofthe operations and functions of data processing system 200 describedherein.

In the depicted example, data processing system 200 employs a hubarchitecture including North Bridge and memory controller hub (NB/MCH)202 and South Bridge and input/output (I/O) controller hub (SB/ICH) 204.Processing unit 206, main memory 208, and graphics processor 210 arecoupled to North Bridge and memory controller hub (NB/MCH) 202.Processing unit 206 may contain one or more processors and may beimplemented using one or more heterogeneous processor systems.Processing unit 206 may be a multi-core processor. Graphics processor210 may be coupled to NB/MCH 202 through an accelerated graphics port(AGP) in certain implementations.

In the depicted example, local area network (LAN) adapter 212 is coupledto South Bridge and I/O controller hub (SB/ICH) 204. Audio adapter 216,keyboard and mouse adapter 220, modem 222, read only memory (ROM) 224,universal serial bus (USB) and other ports 232, and PCI/PCIe devices 234are coupled to South Bridge and I/O controller hub 204 through bus 238.Hard disk drive (HDD) or solid-state drive (SSD) 226 and CD-ROM 230 arecoupled to South Bridge and I/O controller hub 204 through bus 240.PCI/PCIe devices 234 may include, for example, Ethernet adapters, add-incards, and PC cards for notebook computers. PCI uses a card buscontroller, while PCIe does not. ROM 224 may be, for example, a flashbinary input/output system (BIOS). Hard disk drive 226 and CD-ROM 230may use, for example, an integrated drive electronics (IDE), serialadvanced technology attachment (SATA) interface, or variants such asexternal-SATA (eSATA) and micro-SATA (mSATA). A super I/O (SIO) device236 may be coupled to South Bridge and I/O controller hub (SB/ICH) 204through bus 238.

Memories, such as main memory 208, ROM 224, or flash memory (not shown),are some examples of computer usable storage devices. Hard disk drive orsolid-state drive 226, CD-ROM 230, and other similarly usable devicesare some examples of computer usable storage devices including acomputer usable storage medium.

An operating system runs on processing unit 206. The operating systemcoordinates and provides control of various components within dataprocessing system 200 in FIG. 2. The operating system may be acommercially available operating system for any type of computingplatform, including but not limited to server systems, personalcomputers, and mobile devices. An object oriented or other type ofprogramming system may operate in conjunction with the operating systemand provide calls to the operating system from programs or applicationsexecuting on data processing system 200.

Instructions for the operating system, the object-oriented programmingsystem, and applications or programs, such as application 105 in FIG. 1,are located on storage devices, such as in the form of code 226A on harddisk drive 226, and may be loaded into at least one of one or morememories, such as main memory 208, for execution by processing unit 206.The processes of the illustrative embodiments may be performed byprocessing unit 206 using computer implemented instructions, which maybe located in a memory, such as, for example, main memory 208, read onlymemory 224, or in one or more peripheral devices.

Furthermore, in one case, code 226A may be downloaded over network 201Afrom remote system 201B, where similar code 201C is stored on a storagedevice 201D. in another case, code 226A may be downloaded over network201A to remote system 201B, where downloaded code 201C is stored on astorage device 201D.

The hardware in FIGS. 1-2 may vary depending on the implementation.Other internal hardware or peripheral devices, such as flash memory,equivalent non-volatile memory, or optical disk drives and the like, maybe used in addition to or in place of the hardware depicted in FIGS.1-2. In addition, the processes of the illustrative embodiments may beapplied to a multiprocessor data processing system.

In some illustrative examples, data processing system 200 may be apersonal digital assistant (PDA), which is generally configured withflash memory to provide non-volatile memory for storing operating systemfiles and/or user-generated data. A bus system may comprise one or morebuses, such as a system bus, an I/O bus, and a PCI bus. Of course, thebus system may be implemented using any type of communications fabric orarchitecture that provides for a transfer of data between differentcomponents or devices attached to the fabric or architecture.

A communications unit may include one or more devices used to transmitand receive data, such as a modem or a network adapter. A memory may be,for example, main memory 208 or a cache, such as the cache found inNorth Bridge and memory controller hub 202. A processing unit mayinclude one or more processors or CPUs.

The depicted examples in FIGS. 1-2 and above-described examples are notmeant to imply architectural limitations. For example, data processingsystem 200 also may be a tablet computer, laptop computer, or telephonedevice in addition to taking the form of a mobile or wearable device.

Where a computer or data processing system is described as a virtualmachine, a virtual device, or a virtual component, the virtual machine,virtual device, or the virtual component operates in the manner of dataprocessing system 200 using virtualized manifestation of some or allcomponents depicted in data processing system 200. For example, in avirtual machine, virtual device, or virtual component, processing unit206 is manifested as a virtualized instance of all or some number ofhardware processing units 206 available in a host data processingsystem, main memory 208 is manifested as a virtualized instance of allor some portion of main memory 208 that may be available in the hostdata processing system, and disk 226 is manifested as a virtualizedinstance of all or some portion of disk 226 that may be available in thehost data processing system. The host data processing system in suchcases is represented by data processing system 200.

With reference to FIG. 3, this figure depicts a block diagram of anexample configuration 300 in accordance with an illustrative embodiment.The example embodiment includes a neural network application 302. In aparticular embodiment, application 302 is an example of application105A/105B of FIG. 1.

In some embodiments, the neural network application 302 includes atraining module 304, a classification module 306, and a contrastiveexplanations module 308. In alternative embodiments, the neural networkapplication 302 can include some or all of the functionality describedherein but grouped differently into one or more modules. In someembodiments, the functionality described herein is distributed among aplurality of systems, which can include combinations of software and/orhardware based systems, for example Application-Specific IntegratedCircuits (ASICs), computer programs, or smart phone applications.

In some embodiments, the training module 304 generates a classifiermodel based on a DNN. In an embodiment, the DNN is selected from, and/orbased on one or more known deep learning neural networkstructures/systems. In an embodiment, training module 304 includes amodel trainer 316 that trains the DNN using training data 314appropriate for the current domain being modeled. For example, in anembodiment, the classification model is intended to classify articles ofclothing, model trainer 316 trains the classification model using imagesshowing various articles of clothing, for example the well-knownFashion-MNIST fashion product database developed by Zalando SE(Fashion-MNIST or any mark associated with it is the property of ZalandoSE). Also, models generated based on a DNN may be referred to as deeplearning models or deep neural network models (DNN models).

In some embodiments, the training module 304 receives historical datafrom a historical data storage 310 and uses the historical data togenerate a trained machine-learning model for use by the classificationmodule 306. The term “historical data,” as used herein, refers to datathat is familiar to users seeking to train a machine-learning model. Forexample, in some embodiments, the historical data includes a trainingdataset designed to train a machine-learning model that will be able togeneralize enough to accurately make predictions about new data, forexample about features or objects that are not part of the trainingdataset. In some embodiments, the training module 304 receiveshistorical data from a data storage 310 and divides it into a trainingdata set 312 and a testing data set 314 so that the trained model can betested for problems, such as overfitting, before the trained model isready for consumers.

In some embodiments, the training module 304 includes a model trainer316 that receives the training data 314 and tries to “learn” from it bycreating generalized mappings between input and output data for makingpredictions for new inputs where the output variable is unknown. In someembodiments, the model trainer 316 uses any of a variety of knownalgorithms having tunable parameters that are adjusted during thetraining phase to improve the accuracy of the model's predicted outputsfor new inputs.

In some embodiments, the training module 304 includes a model tester 318that monitors the model's ability to make predictions for the testingdata set 312. For example, in some embodiments, the testing data set 312includes data that has not been processed by the machine-learning modelin order to allow the model tester 318 to evaluate the model's abilityto generalize and accurately make predictions about the new data of thehistorical data set 312.

In some embodiments, the classification module 306 receives input imagedata representative of one or more original images. In some embodiments,the input image data, which refers to image data input from a user orother system or application to the classification module 306, forexample from new data storage 322 or image capturing device 324. In anembodiment, input image data is provided to the classification module306 as a real-time data stream. Also, in an embodiment, input image datais a collection of data, for example, data stored in a database, filesystem, or the like, or combination thereof. In an embodiment, theclassification module 306 pre-processes the input image data, orreceives the input image data after pre-processing by another system orapplication, before using the model for classification of the inputimage data. In an embodiment, the pre-processing includes normalizationof data, formatting, cleanup, or the like, or combination thereof.

In some embodiments, the classification module 306 uses the trainedmodel to infer and make predictions about the input image data. Forexample, in some embodiments, the image classifier 320 assigns a classor label to an image. In some embodiments, the image classifier 320assigns a class or label to a group of pixels using a segmentationalgorithm. In an embodiment, the image classifier 320 predictsclassifications for images of the input image data and stores theclassified image data in prediction storage 328. In some embodiments,the image classifier 320 classifies images in the image data accordingto characteristics of pixels or superpixels of images in the image data.

In some embodiments, the contrastive explanations module 308 includesone or both of a Pertinent Positive (PP) generator 330 and a PertinentNegative (PN) generator 332 for generating contrastive explanations thatserve as humanly-interpretable reasons for the classificationpredictions made by the image classifier 320. For example, in someembodiments, image classifier 320 includes a DNN classifier model, andthe contrastive explanations module 308 generates contrastiveexplanations that serve as humanly-interpretable reasons for theclassification predictions made by the DNN classifier model.

In some embodiments, the contrastive explanations module 308automatically generates one or both of a PP image and a PN image foreach original image that is classified by the image classifier 320. Insome embodiments, the PP and PN images are modified versions of theoriginal image. In some embodiments, the PP image is generated byremoving areas of the original image without altering the remainingareas. In some embodiments, the PN image is generated by addinghigh-level features to the original image without altering or removingother areas of the image.

Thus, in some embodiments, the PP generator 330 modifies an originalimage to generate a corresponding pertinent positive image, which is amodified version of the original image in which modifications arelimited to removing areas of the original image. Also, in someembodiments, the PN generator 332 modifies an original image to generatea corresponding pertinent negative image, which is a modified version ofthe original image in which modifications are limited to adding one ormore high-level features.

In some embodiments, the PP image and the PN image provide visual cuesindicative of image properties that were influential to the DNNclassifier for its classification prediction for the original image. Insome embodiments, the PN and PP images are solutions to respectiveoptimization problems that are discussed in greater detail in connectionwith FIG. 4 below. For example, in some embodiments, to generate the PPimage, the PP generator 330 searches for the smallest area of theoriginal image that will still get the same classification by the DNNclassifier as that of the original image. Also, in some embodiments, togenerate the PN image, the PN generator 332 searches for the smallestarea of the original image that can be changed (by addition ofhigh-level feature(s)) to get a new classification by the DNN classifierthat differs from that of the original image. Stated another way, the PNgenerator 332 searches for high-level feature(s) that cause the smallestchange to the original image but still cause the DNN classifier tochange the classification of the modified original image.

Thus, the PP image shows the area(s) of the original image that wereinfluential to the DNN classifier because the displayed areas are thosethat need to remain in the original image to prevent the DNN fromchanging its classification. On the other hand, the PN image showsmodified area(s) (as added high-level features) of a modified originalimage that were influential to the DNN classifier because the modifiedareas are those that need to remain modified in the modified originalimage to prevent the DNN from changing its classification back to thatof the original image.

In some embodiments, the contrastive explanations module 308 onlygenerates one or both of a PP image and a PN image original images wheninstructed to do so, for example based on user inputs or softwareinstructions. In some embodiments, the contrastive explanations module308 generates one or both of a PP version and a PN version of anoriginal image in parallel with the classification of the original imageby the image classifier 320. In some embodiments, the contrastiveexplanations module 308 generates one or both of a PP version and a PNversion of an original image any time after image classifier 320classifies the original image, but only while the original image and itsclassification are available, or can be provided to, the neural network.

In some embodiments, the PN generator 332 uses high-level features fromfeatures storage 322. In some embodiments, the features storage 322 is athird-party image database or other image provider of any kind. In someembodiments, the features storage 322 is a remote or external computermemory that stores the high-level features. In some embodiments, the PNgenerator 332 uses high-level features that are learned high-levelfeatures (i.e., disentangled representations). For example, in someembodiments, the model trainer 316 uses unsupervised training thatresults in a collection of high-level features learned from images inthe training data set 314. Alternatively, in some embodiments, thefeature generator 338 is a separate model trainer that uses unsupervisedtraining to generate a collection of high-level features that are passedto the PN generator 332 for use in generating the PN images. In someembodiments, the feature generator 338 is a separate model trainer thatuses a supervised extraction technique, where people manually labelhigh-level features that are extracted to generate a collection ofhigh-level features that are passed to the PN generator 332 for use ingenerating the PN images.

In some embodiments, the PP generator 330 stores generated PP images inPP storage 334, and the PN generator 332 stores generated PN images inPN storage 340. Once the classified image, PP image, and PN image areready (or the classified image and one of the PP image and PN image areready), the information is provided to report generator 342, which thengenerates data that can be used as a report for informing users aboutthe classification of an original image, and contrasting explanationsfor the image's classifications in the form of one or both of the PN andPP images. The report data 346 output by the report generator 342 can bein any desired format, for example, xml, csv, json, pdf, or others.

With reference to FIG. 4, this figure depicts a flowchart of an exampleprocess 400 for classifying data using machine learning that generatescontrastive explanations in accordance with an illustrative embodiment.In a particular embodiment, the neural network application 302 carriesout the process 400. In an embodiment, the process 400 uses a DNN modelto classify image data. In an embodiment, a DNN model is aclassification model that requires training times that increase inexchange for more accurate predictions. However, in some embodiments,machine learning and/or classification techniques other than a DNN.

In an embodiment, at block 402, neural network application 302 generatesa classifier model based on a DNN. In an embodiment, the DNN is selectedfrom, and/or based on one or more known deep learning neural networkstructures/systems. In an embodiment, neural network application 302trains the DNN using training data appropriate for the current domainbeing modeled. For example, in an embodiment, the classification modelis intended to classify articles of clothing, neural network application302 trains the classification model using images showing variousarticles of clothing, for example the well-known Fashion-MNIST fashionproduct database developed by Zalando SE. Also, models generated basedon a DNN may be referred to as deep learning models or deep neuralnetwork models (DNN models).

In an embodiment, at block 404, once the model is trained, neuralnetwork application 302 employs the model to classify input image datarepresentative of one or more original input images (or “originalimages”). In some embodiments, the input image data, which refers toimage data input from a user or other system or application to theneural network application 302. In an embodiment, input image data isprovided to the neural network application 302 as a real-time datastream. Also, in an embodiment, input image data is a collection ofdata, for example, data stored in a database, file system, or the like,or combination thereof. In an embodiment, the neural network application302 pre-processes the input image data, or receives the input image dataafter pre-processing by another system or application, before using themodel for classification of the input image data. In an embodiment, thepre-processing includes normalization of data, formatting, cleanup, orthe like, or combination thereof.

In some embodiments, at block 406, the image classifier 320 uses thetrained model to infer and make predictions about the each of theoriginal input images in the input image data. For example, in someembodiments, the image classifier 320 assigns a class or label to eachoriginal input image. In some embodiments, the image classifier 320assigns a class or label to a group of pixels using a segmentationalgorithm. In an embodiment, the image classifier 320 predicts aclassification for each original input image of the input image data andstores the classified image data in computer memory. In someembodiments, the image classifier 320 classifies images in the imagedata according to characteristics of pixels or superpixels of images inthe image data.

In an embodiment, at blocks 408 and 410, the neural network application302 generates contrastive explanations that serve as ahumanly-interpretable reasons for the DNN's classification of theoriginal input images. In some embodiments, the neural networkapplication generates contrastive explanations for grayscale images,monochromatic images, and color images. In an embodiment, the neuralnetwork application 302 creates two types of contrastive explanations: a“Pertinent Negative” (or “PN”) image at block 408 and a “PertinentPositive” (or “PP”) image at block 410.

A pertinent positive image is a modified version of the original inputimage, where the modifications are limited to removing portions of theoriginal image and nothing is added. The pertinent positive image showsthe smallest area of the original image that will still get the sameclassification by the DNN classifier as that of the original image.Thus, the pertinent positive image shows the areas of the original imagethat were significantly influential to the DNN classifier, and thereforeprovides some insight into why the DNN made the prediction that it made.

As a simple example, a pertinent negative of a grayscale image of anumber “3” might be a vertical line, because the addition of a verticallike “1” to an image of a number “3” might result in re-classificationof the image as a capital “B.” If another possible class is the number“88,” another potential pertinent negative would be the number followedby a capital epsilon “8E.” There are multiple potential pertinentnegatives, but the actual pertinent negative image is a modified versionof the original image that satisfies this criteria:

-   -   (1) At least one high-level feature has been added to the        original image;    -   (2) No portion of the original image has been removed;    -   (3) The DNN used at block 406 classifies this modified version        of the original image in a class that is different from that of        the original image; and    -   (4) Compared to all other modified versions of the original        image that were created to satisfy (1) through (3), the        pertinent negative image is most similar to the original image.        In other words, the modified version (i.e., modified by adding a        high level feature) of the original image that is most like the        original image while having a different classification is the PN        image.

To identify pertinent negatives, addition is simpler to define forgrayscale images where a pixel with a value of “0” indicates noinformation and increasing the pixel value towards “1” indicatesaddition. However, for colored images with rich structure, there is nota clear “no information” value for a pixel. Therefore, defining an“addition” for a pixel value is not straight-forward and is unlikely toresult in an intuitive result. Defining addition in a naive way, such assimply increasing the pixel or red-green-blue (RGB) channel intensitiesleads to uninterpretable images as the relative structure may not bemaintained with the added portion being not necessarily interpretable.Moreover, even for grayscale images, just increasing values of pixelsmay not lead to humanly interpretable images or, if it is aninterpretable image, the added portion will not necessarily be readilyascertainable to a human observer. Therefore, embodiments disclosedherein utilize high-level features as “additions.” These high-levelfeature explanations provide an intuitive and humanly interpretable formof evidence that leads to realistic images with the additions also beinginterpretable to help explain why the model made the classificationchoices that it made.

Deep learning that utilizes a Convolutional Neural Network (CNN)segments data using convolutional filters to locate and identifylearned, observable features in the data. Each filter or layer of theCNN architecture transforms the input data to increase the selectivityand invariance of the data. This abstraction of the data allows theneural network application to focus on the features in the data it isattempting to classify and ignore irrelevant background information.Deep learning operates on the understanding that many datasets includehigh level features which include low level features. While examining animage, for example, rather than looking for an object, it is moreefficient to look for edges, which form motifs, which form parts, whichform the object being sought. These hierarchies of features can be foundin many different forms of data, such as speech and text, etc. Learnedobservable features include objects and quantifiable regularitieslearned by the machine.

In an embodiment, at block 408, the neural network application 302creates a pertinent negative image by searching for an addition to animage, where the addition is a high-level feature that, if added to theoriginal image, would be a smallest change that could be made to theimage that would change the image's classification. In an embodiment, analgorithm for finding the pertinent negative includes the followingnotation:

-   -   χ denotes the feasible input space with (x₀, t₀) being an        example such that x₀∈χ and t₀ is the predicted label obtained        from a neural network classifier.    -   S denotes the set of superpixels that partition x₀ with        denoting a set of binary masks which when applied to x₀ produce        images        (x₀) by selecting the corresponding superpixels from S.    -   M_(x) denotes the mask corresponding to image x=M_(x)(x₀).    -   D(.) denotes the data manifold (based on a Generative        adversarial network (GAN) or a variational autoencoder (VAE)).    -   denotes the latent representation with        _(x) denoting the latent representation corresponding to input x        such that x=D(        _(x)).    -   k denotes the number of (available or learned) interpretable        features (latent or otherwise) which represent meaningful        concepts (viz. moustache, glasses, smile) and g_(i)(.), ∀i∈{1, .        . . , k}, are corresponding functions acting on these features        with higher values indicating presence of a certain visual        concept while lower values indicating its absence.

For example, suppose a KitchenEquip data set were created that includedseveral thousand images of kitchen equipment, including images ofplates, stock pots, mixing bowls, and ladles. Such a data set could havemany potential different high-level (interpretable) features that couldbe used to differentiate one item from another. For example, thehigh-level features could include side walls and handles, where sidewalls distinguish the stock pots from plates and handles distinguish theladles from mixing bowls. Such high-level features could potentially beused to build binary classifiers for each of the features, for examplewhere a “1” indicates the presence of the feature and a “0” indicatesthe absence of the feature. These classifiers would be the g_(i)(.)functions. On the other hand, for datasets with no high-levelinterpretable features, we could find latents by learning disentangledrepresentations and choose those latents (with ranges) that areinterpretable. Here the g_(i) functions would be an identity map ornegative identity map depending on which direction adds a certainconcept (viz. sleeveless shirt to a long sleeve one). In an embodiment,these attribute functions are used as latent features for the generatorin a causal graph, or given a causal graph for the desired attributes,the neural network application 302 learns these functions using knownmethods.

In an embodiment, the neural network application 302 follows a procedurefor finding Pertinent Negatives that involves solving an optimizationproblem over the variable 6 which is the outputted image. In anembodiment, the neural network application outputs the classificationprediction f(x) of the classifier model for an example image x, wheref(⋅) is any function that outputs a vector of prediction scores for allclasses, such as prediction probabilities and logits (unnormalizedprobabilities) that are widely used in neural networks.

In an embodiment, the neural network application finds a pertinentnegative that results in the creation of a discernible image that theDNN predicts to be in a different class than the original input imageand where a minimal number of things have been “added” to the originalinput image without deleting anything to obtain the new image. If theneural network application finds such an image, the things that areadded to the input image are referred to as the pertinent negatives. Themodified input image having the pertinent negatives added is referred toas the pertinent negative image.

In an embodiment, the neural network application searches for thepertinent negatives using high-level interpretable features availablefor the dataset. Multiple public datasets have high-level interpretablefeatures, while for others such features can be learned usingclassifiers for k high-level features, defined as functions g_(i)(.),∀i∈{1, . . . , k}, where in each of these functions, a higher valueindicates addition of a feature and a lower value indicates absence of afeature. In an embodiment, the neural network application uses thesefunctions to define addition as introducing more concepts into an imagewithout deleting any existing concepts. Formally, this corresponds tonever decreasing the g_(i)(.) from their original values based on theinput image, but rather increasing them. The neural network applicationalso seeks the class-changing high-level feature that results in aminimal number of additions to the input image, which corresponds to asfew g_(i)(.) as possible to increase in value (within their allowedranges) that will result in the final image being in a different class.The neural network application also seeks a pertinent negative imagethat is realistic, or at least discernable, so the neural networkapplication learns a manifold D on which it perturbs the image, as itseeks a final pertinent negative image to also lie on the manifold Dafter the additions. In an embodiment, the above goals and conditionsgive rise to the following optimization problem:

$\begin{matrix}{{\min\limits_{\delta \in \mathcal{X}}{\gamma{\sum\limits_{i}{\max\left\{ {{{g_{i}\left( x_{0} \right)} - {g_{i}\left( {\mathcal{D}\left( z_{\delta} \right)} \right)}},0} \right\}}}}} + {\beta{{g\left( {\mathcal{D}\left( z_{\delta} \right)} \right)}}_{1}} - {{c \cdot \min}\left\{ {{{\max\limits_{i \neq t_{0}}\left\lbrack {f(\delta)} \right\rbrack_{i}} - \left\lbrack {f(\delta)} \right\rbrack_{t_{0}}},\kappa} \right\}} + {\eta{{x_{0} - {\mathcal{D}\left( z_{\delta} \right)}}}_{2}^{2}} + {v{{{z_{x_{0}} - z_{\delta}}}_{2}^{2}.}}} & (1)\end{matrix}$

The first term in the objective function (1) above encourages theaddition of high-level features g_(i)(.)s for the final image withoutbeing less than their original values. The second term encouragesminimal addition of interpretable features. The third term is a designedloss function that encourages the modified image δ to be predicted bythe DNN classifier model as a different class than the input imaget₀=arg max_(i)[f(x₀)]_(i), where [f(δ)]_(i) is the i-th class predictionscore of δ. The hinge-like loss function pushes the modified input imageδ to lie in a different class than x₀. The parameter κ≥0 is a confidenceparameter that controls the separation between [f(δ)]_(t) ₀ andmax_(i≠t) ₀ [f(δ)]_(i). The fourth (η>0) and fifth terms (ν>0) encouragethe final image to be close to the original image in the input andlatent spaces. In an embodiment, the neural network application 302 hasa threshold for each of the high-level features g_(i)(.)s, where only anincrease in value beyond that threshold would imply a meaningfuladdition. The advantage of defining addition in this manner is that notonly are the final images interpretable, but so are the additions, andwe can clearly elucidate which (concepts) should be necessarily absentto maintain the original classification.

In an embodiment, the neural network application solves for pertinentnegatives using the objective function (1). The L₁ regularization termis penalizing a non-identity and complicated function ∥g(D(

_(δ)))∥₁ of the optimization variable 6 involving the data manifold D,so proximal methods are not applicable. Instead, neural networkapplication uses a large number of iterations (e.g., in a range from 500to 1500 iterations, such as 1000 intervals) of standard subgradientdescent to solve the function (1). In an embodiment, the neural networkapplication finds a pertinent negative by setting it to be the iteratehaving the smallest L₂ distance ∥

_(x0)−

_(δ)∥₂ to the latent code of x₀, among all iterates where predictionscore of solution δ* is at least [f(x₀)]_(t) ₀ .

In an embodiment, the process [FIG. 6] To identify pertinent negatives.In an embodiment, at block 410, the neural network application 302creates a pertinent positive image by searching for a minimal set ofimportant pixels or superpixels which by themselves are sufficient forthe classifier to output the same class as the original example. Moreformally, for an example image x₀, our goal is to find an image δ∈

(x₀) such that argmax_(i)[Pred(x₀)]_(i)=argmax_(i)[Pred(δ)]_(i) (i.e.same prediction), with δ containing as few superpixels and interpretableconcepts from the original image as possible. This leads to thefollowing optimization problem:

$\begin{matrix}{{\min\limits_{\delta \in {\mathcal{M}{(x_{0})}}}{\gamma{\sum\limits_{i}{\max\left\{ {{{g_{i}(\delta)} - {g_{i}\left( x_{0} \right)}},0} \right\}}}}} - {{c \cdot \min}\left\{ {{\left\lbrack {f(\delta)} \right\rbrack_{t_{0}} - {\max\limits_{i \neq t_{0}}\left\lbrack {f(\delta)} \right\rbrack_{i}}},\kappa} \right\}} + {\beta{{M_{\delta}}_{1}.}}} & (2)\end{matrix}$

The first term in the objective function (2) above penalizes theaddition of attributes to encourage a sparse pertinent positiveexplanation. The second term is a designed loss function that encouragesthe modified image δ to be predicted by the DNN classifier model as asame class as the input image and is minimized when [f(δ)]_(t) ₀ isgreater than max_(i≠t) ₀ [f(δ)]_(i) by at least κ≥0, which is amargin/confidence parameter. Parameters γ, c, β≥0 are the associatedregularization coefficients.

In an embodiment, the neural network application uses the aboveformulation to optimize over superpixels, which subsumes the case ofjust using pixels, to provide more interpretable results on imagedatasets.

In an embodiment, the neural network application solves for pertinentpositives using the objective function (2) by first relaxing the binarymask M_(δ) on superpixels to be real-valued (each entry is between [0,1]) and then apply an algorithm to solve such optimization problems, forexample the well-known standard Iterative Soft Thresholding Algorithm(ISTA) that efficiently solves optimization problems with L₁regularization. In an embodiment, the neural network application runsseveral iterations (e.g., in a range of 70 to 130 iterations, such as100 iterations) of ISTA and obtains a solution M_(δ*) that has thesmallest L₁ norm and satisfies the prediction of δ* being within marginκ of at least [f(x₀)]_(t) ₀ , and then ranks the entries in M_(δ*)according to their values in descending order and subsequently addsranked superpixels until the DNN classifier model predicts masked imageis predicts [f(x₀)]_(t) ₀ .

With reference to FIG. 5, this figure depicts a block diagram of anembodiment of an output report 500 generated by the neural networkapplication 302 for reporting the results of a classification processthat includes generating contrastive explanations in accordance with anillustrative embodiment. In an embodiment the report 500 includes threerepeating rows: classification row 502, image row 504, and contrastiveexplanations row 506. In an embodiment, the report 500 includes threecolumns: input image column 508, pertinent negative column 510, andpertinent positive column 512.

In an embodiment, the block at the intersection of image row 504 andinput image column 508 shows an input image, for example as input atblock 504 in FIG. 3. The block at the intersection of classification row502 and input image column 508 shows the classification predicted by aclassifier model for the corresponding input image, for example aspredicted by the DNN classifier model at block 506 in FIG. 3. The blockat the intersection of contrastive explanations row 506 and pertinentnegative column 510 shows an attribute (e.g., high-level feature) thatresulted from a process for finding pertinent negatives, for example asfound at block 408 in FIG. 4. The block at the intersection of image row504 and pertinent negative column 510 shows a pertinent negative image,which is a modified version of the input image that has been altered toinclude the corresponding pertinent negative. The block at theintersection of classification row 502 and pertinent negative column 510shows the classification predicted by a classifier model for thecorresponding pertinent negative image. The block at the intersection ofcontrastive explanations row 506 and pertinent positive column 512 showsa number of features (e.g., superpixels) that resulted from a processfor finding pertinent positives, for example as found at block 410 inFIG. 4. The block at the intersection of image row 504 and pertinentpositive column 512 shows a pertinent positive image, which is amodified version of the input image that includes only the minimumportions of the input image that can still result in it being classifiedthe same as the input image. The block at the intersection of thepertinent positive column 512 and the classification row 502 is not usedbecause the pertinent positive image will, by definition, have the sameclassification as the input image. The block at the intersection of thecontrastive explanations row 506 and input image column 508 is not usedbecause there is no contrastive explanation information generated duringthe initial input and classification stage of the overall process.

The report 500 provides an intuitive and human-readable explanation toaid in understanding decisions made by the classifier. For example, thefirst image row 502 shows an input image classified as “Shirt.” Thepertinent negative image has a new classification that is “coat” and thepertinent negative feature that was added was “wider sleeves, waist.”This indicates that the classifier model focused on the portion of theimage around the sleeves and waistline to determine whether the image isa shirt or coat. The pertinent positive image also provides insight intothe decision-making process of the classifier. The classifier requiresat least 15 superpixel/features to classify this image as “Shirt” andmuch of the decision was based on portions of the image around thecollar and buttons.

As another example, the second image row 502 shows an input imageclassified as “Trouser.” The pertinent negative image has a newclassification that is “Dress” and the pertinent negative features thatwere added was “middle piece of fabric.” This indicates that theclassifier model focused on the gap portion between the trouser legs todetermine whether the image is a trouser or dress. The pertinentpositive image also supports this conclusion because about half of theoriginal image remains, which is enough to begin to see the separatetrouser legs.

With reference to FIG. 6 this figure depicts a flowchart of an exampleprocess 600 for creating a PN image in accordance with an illustrativeembodiment. In a particular embodiment, the PN generator 332 carries outthe process 600. In an embodiment, the process 600 uses a set of khigh-level features g_(i)(.), ∀i∈{1, . . . , k}, to modify respectiveduplicates of the original image (i=1 to k) to identify a modifiedoriginal image that is most similar to the original image but classifieddifferently by the DNN.

In an embodiment, at block 602, the process obtains a copy of theoriginal input image. Next, at block 604, the process uses high levelfeature g_(i)(.), to create a modified image (i) by adding high levelfeature g_(i)(.) to original image. For example, in an embodiment theoriginal input image is a mixing bowl and the high-level featureg_(i)(.) is a pan handle, the original input image is modified to show amixing bowl having a pan handle. Next, at block 606, the DNN classifierpredicts a class for the modified image. Following the previous examplewhere an image of a mixing bowl was modified to have a pan handle, insome embodiments the DNN that correctly classified the mixing bowl as amixing bowl will classify the modified image as a wok rather than as amixing bowl because of the addition of the handle. In other embodiments,the pan handle is not enough to cause the DNN to classify the mixingbowl differently. At block 608, the process determines whether themodified image has a classification that is different from that of theoriginal image. If so, the process continues to block 610 where thecounter i is incremented. If not, the process continues to block 612,where the process checks whether this modified image is the onlymodified image to have been classified differently than the originalimage. If so, the process continues to block 614 where the processstores the modified image (i) in electronic memory as a potential PNimage. Otherwise, the process continues to block 616. At block 616, theprocess calculates the difference between modified image (i) and theoriginal input image. At block 618, the process determines whether themodified image (i) is more similar to the original input image than thenstored potential PN image. If so, then the process continues to block614 where the process stores the modified image (i) in electronic memoryas a potential PN image. In some embodiments, any previous potential PNimage is overwritten or otherwise deleted.

In some embodiments, after block 614, the process continues to block 610where the counter i is incremented. In some embodiments, if there arestill high level features to check (i≤k), the process continues back tothe beginning at block 602. Otherwise, the process continues to block620 where the modified image remaining stored as the potential PN imageis considered the PN image.

With reference to FIG. 7 this figure depicts a flowchart of an exampleprocess 700 for creating a PP image in accordance with an illustrativeembodiment. In a particular embodiment, the PP generator 330 carries outthe process 700. In an embodiment, the process 700 uses an optimizationalgorithm to iteratively remove portions of a copy of the original inputimage and use the DNN to predict the classification of the modifiedimage, which continues until the DNN no longer classifies the modifiedimage to have the same class as the original image. The last version ofthat modified image that still had the same class as the original imageis saved in an array of other copies of the original image that wentthrough the same process, but with different patterns removed. The finalPP image is selected from that array.

In an embodiment, at block 702, the process obtains a copy of theoriginal input image. Next, at block 704, the process creates a modifiedimage by removing a portion of the image. In some embodiments, theprocess removes selected pixels from the image. In some embodiments, theprocess removes selected superpixels or groups of superpixels from theimage. Next, at block 706, the DNN classifier predicts a class for themodified image. At block 708, the process determines whether themodified image has a classification that is different from that of theoriginal image. If the classification is still the same (“No” at block708), the process continues to block 710 where a copy of the modifiedimage is stored. In some embodiments, if a less-modified image is storedfrom a previous iteration of the loop from block 706 to 712, the currentimage overwrites the previously-stored image so that the stored image isalways an image that has been most heavily modified without beingreclassified at block 708. Next, at block 712, the process removes moreof the modified image. The process then loops back to block 706, wherethe DNN classifier predicts a class for the modified image.

Eventually the image will have been modified to such an extent that theDNN will predict a different class for the modified image. At thispoint, the process continued to block 724, where the image stored atblock 710 to verify whether it satisfies other parameters, such as Lregularization parameters. If so, the image is added to an array ofimages obtained from the process from block 702 to 712. At block 716, analgorithm controller determines whether to continue with another copy ofthe original image by returning to block 702. Otherwise, the processcontinues to block 718, where the array of saved images is sorted tofind an image having more recognizable results in a smallest remainingportion of the original input image. At block 720, the image bestsatisfying the criteria is output as the PP image.

The following definitions and abbreviations are to be used for theinterpretation of the claims and the specification. As used herein, theterms “comprises,” “comprising,” “includes,” “including,” “has,”“having,” “contains” or “containing,” or any other variation thereof,are intended to cover a non-exclusive inclusion. For example, acomposition, a mixture, process, method, article, or apparatus thatcomprises a list of elements is not necessarily limited to only thoseelements but can include other elements not expressly listed or inherentto such composition, mixture, process, method, article, or apparatus.

Additionally, the term “illustrative” is used herein to mean “serving asan example, instance or illustration.” Any embodiment or designdescribed herein as “illustrative” is not necessarily to be construed aspreferred or advantageous over other embodiments or designs. The terms“at least one” and “one or more” are understood to include any integernumber greater than or equal to one, i.e. one, two, three, four, etc.The terms “a plurality” are understood to include any integer numbergreater than or equal to two, i.e. two, three, four, five, etc. The term“connection” can include an indirect “connection” and a direct“connection.”

References in the specification to “one embodiment,” “an embodiment,”“an example embodiment,” etc., indicate that the embodiment describedcan include a particular feature, structure, or characteristic, butevery embodiment may or may not include the particular feature,structure, or characteristic. Moreover, such phrases are not necessarilyreferring to the same embodiment. Further, when a particular feature,structure, or characteristic is described in connection with anembodiment, it is submitted that it is within the knowledge of oneskilled in the art to affect such feature, structure, or characteristicin connection with other embodiments whether or not explicitlydescribed.

The terms “about,” “substantially,” “approximately,” and variationsthereof, are intended to include the degree of error associated withmeasurement of the particular quantity based upon the equipmentavailable at the time of filing the application. For example, “about”can include a range of ±8% or 5%, or 2% of a given value.

The descriptions of the various embodiments of the present inventionhave been presented for purposes of illustration but are not intended tobe exhaustive or limited to the embodiments disclosed. Manymodifications and variations will be apparent to those of ordinary skillin the art without departing from the scope and spirit of the describedembodiments. The terminology used herein was chosen to best explain theprinciples of the embodiments, the practical application or technicalimprovement over technologies found in the marketplace, or to enableothers of ordinary skill in the art to understand the embodimentsdescribed herein.

The descriptions of the various embodiments of the present inventionhave been presented for purposes of illustration but are not intended tobe exhaustive or limited to the embodiments disclosed. Manymodifications and variations will be apparent to those of ordinary skillin the art without departing from the scope and spirit of the describedembodiments. The terminology used herein was chosen to best explain theprinciples of the embodiments, the practical application or technicalimprovement over technologies found in the marketplace, or to enableothers of ordinary skill in the art to understand the embodimentsdescribed herein.

Thus, a computer implemented method, system or apparatus, and computerprogram product are provided in the illustrative embodiments formanaging participation in online communities and other related features,functions, or operations. Where an embodiment or a portion thereof isdescribed with respect to a type of device, the computer implementedmethod, system or apparatus, the computer program product, or a portionthereof, are adapted or configured for use with a suitable andcomparable manifestation of that type of device.

Where an embodiment is described as implemented in an application, thedelivery of the application in a Software as a Service (SaaS) model iscontemplated within the scope of the illustrative embodiments. In a SaaSmodel, the capability of the application implementing an embodiment isprovided to a user by executing the application in a cloudinfrastructure. The user can access the application using a variety ofclient devices through a thin client interface such as a web browser(e.g., web-based e-mail), or other light-weight client-applications. Theuser does not manage or control the underlying cloud infrastructureincluding the network, servers, operating systems, or the storage of thecloud infrastructure. In some cases, the user may not even manage orcontrol the capabilities of the SaaS application. In some other cases,the SaaS implementation of the application may permit a possibleexception of limited user-specific application configuration settings.

The present invention may be a system, a method, and/or a computerprogram product at any possible technical detail level of integration.The computer program product may include a computer readable storagemedium (or media) having computer readable program instructions thereonfor causing a processor to carry out aspects of the present invention.

The computer readable storage medium can be a tangible device that canretain and store instructions for use by an instruction executiondevice. The computer readable storage medium may be, for example, but isnot limited to, an electronic storage device, a magnetic storage device,an optical storage device, an electromagnetic storage device, asemiconductor storage device, or any suitable combination of theforegoing. A non-exhaustive list of more specific examples of thecomputer readable storage medium includes the following: a portablecomputer diskette, a hard disk, a random access memory (RAM), aread-only memory (ROM), an erasable programmable read-only memory (EPROMor Flash memory), a static random access memory (SRAM), a portablecompact disc read-only memory (CD-ROM), a digital versatile disk (DVD),a memory stick, a floppy disk, a mechanically encoded device such aspunch-cards or raised structures in a groove having instructionsrecorded thereon, and any suitable combination of the foregoing. Acomputer readable storage medium, as used herein, is not to be construedas being transitory signals per se, such as radio waves or other freelypropagating electromagnetic waves, electromagnetic waves propagatingthrough a waveguide or other transmission media (e.g., light pulsespassing through a fiber-optic cable), or electrical signals transmittedthrough a wire.

Computer readable program instructions described herein can bedownloaded to respective computing/processing devices from a computerreadable storage medium or to an external computer or external storagedevice via a network, for example, the Internet, a local area network, awide area network and/or a wireless network. The network may comprisecopper transmission cables, optical transmission fibers, wirelesstransmission, routers, firewalls, switches, gateway computers and/oredge servers. A network adapter card or network interface in eachcomputing/processing device receives computer readable programinstructions from the network and forwards the computer readable programinstructions for storage in a computer readable storage medium withinthe respective computing/processing device.

Computer readable program instructions for carrying out operations ofthe present invention may be assembler instructions,instruction-set-architecture (ISA) instructions, machine instructions,machine dependent instructions, microcode, firmware instructions,state-setting data, configuration data for integrated circuitry, oreither source code or object code written in any combination of one ormore programming languages, including an object oriented programminglanguage such as Smalltalk, C++, or the like, and procedural programminglanguages, such as the “C” programming language or similar programminglanguages. The computer readable program instructions may executeentirely on the user's computer, partly on the user's computer, as astand-alone software package, partly on the user's computer and partlyon a remote computer or entirely on the remote computer or server. Inthe latter scenario, the remote computer may be connected to the user'scomputer through any type of network, including a local area network(LAN) or a wide area network (WAN), or the connection may be made to anexternal computer (for example, through the Internet using an InternetService Provider). In some embodiments, electronic circuitry including,for example, programmable logic circuitry, field-programmable gatearrays (FPGA), or programmable logic arrays (PLA) may execute thecomputer readable program instructions by utilizing state information ofthe computer readable program instructions to personalize the electroniccircuitry, in order to perform aspects of the present invention.

Aspects of the present invention are described herein with reference toflowchart illustrations and/or block diagrams of methods, apparatus(systems), and computer program products according to embodiments of theinvention. It will be understood that each block of the flowchartillustrations and/or block diagrams, and combinations of blocks in theflowchart illustrations and/or block diagrams, can be implemented bycomputer readable program instructions.

These computer readable program instructions may be provided to aprocessor of a general purpose computer, special purpose computer, orother programmable data processing apparatus to produce a machine, suchthat the instructions, which execute via the processor of the computeror other programmable data processing apparatus, create means forimplementing the functions/acts specified in the flowchart and/or blockdiagram block or blocks. These computer readable program instructionsmay also be stored in a computer readable storage medium that can directa computer, a programmable data processing apparatus, and/or otherdevices to function in a particular manner, such that the computerreadable storage medium having instructions stored therein comprises anarticle of manufacture including instructions which implement aspects ofthe function/act specified in the flowchart and/or block diagram blockor blocks.

The computer readable program instructions may also be loaded onto acomputer, other programmable data processing apparatus, or other deviceto cause a series of operational steps to be performed on the computer,other programmable apparatus or other device to produce a computerimplemented process, such that the instructions which execute on thecomputer, other programmable apparatus, or other device implement thefunctions/acts specified in the flowchart and/or block diagram block orblocks.

The flowchart and block diagrams in the Figures illustrate thearchitecture, functionality, and operation of possible implementationsof systems, methods, and computer program products according to variousembodiments of the present invention. In this regard, each block in theflowchart or block diagrams may represent a module, segment, or portionof instructions, which comprises one or more executable instructions forimplementing the specified logical function(s). In some alternativeimplementations, the functions noted in the blocks may occur out of theorder noted in the Figures. For example, two blocks shown in successionmay, in fact, be executed substantially concurrently, or the blocks maysometimes be executed in the reverse order, depending upon thefunctionality involved. It will also be noted that each block of theblock diagrams and/or flowchart illustration, and combinations of blocksin the block diagrams and/or flowchart illustration, can be implementedby special purpose hardware-based systems that perform the specifiedfunctions or acts or carry out combinations of special purpose hardwareand computer instructions.

What is claimed is:
 1. A computer implemented method for generatingcontrastive information for a classifier prediction, the computerimplemented method comprising: receiving, by one or more processors,image data representative of an original input image; creating, by theone or more processors, a modified input image by adding a high-levelfeature to a copy of the original input image; and determining, by theone or more processors, using a deep learning classifier model, that themodified input image is a pertinent-negative image that is most similarto the original input image in a set of modified input images, whereinthe modified input image has a classification that is different from aclassification of the original input image.
 2. The computer implementedmethod of claim 1, further comprising: generating, by the one of moreprocessors, a report that includes a visual representation of thepertinent-negative image.
 3. The computer implemented method of claim 1,further comprising: creating, by the one or more processors, apertinent-positive image that is a modified version of the originalinput image and that includes fewer than all superpixels of the originalinput image while still being predicted by the deep learning classifiermodel to be in the classification of the original input image.
 4. Thecomputer implemented method of claim 3, further comprising: comparing aplurality of modified images to identify a candidate modified image thathas an amount of the original input image remaining while still beingclassified in the classification of the original input image, whereineach of the plurality of modified images is a modified version of theoriginal input image having fewer than all portions of the input image.5. The computer implemented method of claim 1, wherein the determiningof the pertinent-negative image includes determining that thepertinent-negative image is a result with a smallest change to theoriginal input image from among other potential modifications to theoriginal input image.
 6. The computer implemented method of claim 1,wherein the original input image is a multiple-color image.
 7. Thecomputer implemented method of claim 1, wherein the determining includesidentifying that the pertinent-negative image will be classified by thedeep learning classifier model as a second classification that isdifferent from a first classification of the original input image.
 8. Acomputer usable program product for generating contrastive informationfor a classifier prediction, the computer usable program productcomprising a computer-readable storage device, and program instructionsstored on the storage device, the stored program instructionscomprising: program instructions to receive, by one or more processors,image data representative of an original input image; programinstructions to create, by the one or more processors, a modified inputimage by adding a high-level feature to a copy of the original inputimage; and program instructions to determine, by the one or moreprocessors, using a deep learning classifier model, that the modifiedinput image is a pertinent-negative image that is most similar to theoriginal input image in a set of modified input images, wherein themodified input image has a classification that is different from aclassification of the original input image.
 9. A computer usable programproduct of claim 8, further comprising program instructions to generate,by the one or more processors, a report that includes a visualrepresentation of the pertinent-negative image.
 10. A computer usableprogram product of claim 8, further comprising: program instructions tocreate, by the one or more processors, a pertinent-positive image thatis a modified version of the original input image and that includesfewer than all superpixels of the original input image while still beingpredicted by the deep learning classifier model to be in theclassification of the original input image.
 11. A computer usableprogram product of claim 10, further comprising: program instructions tocompare a plurality of modified images to identify a candidate modifiedimage that has an amount of the original input image remaining whilestill being classified in the classification of the original inputimage, wherein each of the plurality of modified images is a modifiedversion of the original input image having fewer than all portions ofthe input image.
 12. A computer usable program product of claim 8,wherein the program instructions to determine the pertinent-negativeimage includes program instructions to determine that thepertinent-negative image is a result with a smallest change to theoriginal input image from among other potential modifications to theoriginal input image.
 13. A computer usable program product of claim 8,wherein the input image is a multiple-color image.
 14. A computer usableprogram product of claim 8, wherein the program instructions todetermine includes program instructions to identify that thepertinent-negative image will be classified by the deep learningclassifier model as a second classification that is different from afirst classification of the original input image.
 15. A computer systemcomprising a processor, a computer-readable memory, and acomputer-readable storage device, and program instructions stored on thestorage device for execution by the processor via the memory, the storedprogram instructions comprising: program instructions to receive, by oneor more processors, image data representative of an original inputimage; program instructions to create, by the one or more processors, amodified input image by adding a high-level feature to a copy of theoriginal input image; and program instructions to determine, by the oneor more processors, using a deep learning classifier model, that themodified input image is a pertinent-negative image that is most similarto the original input image in a set of modified input images, whereinthe modified input image has a classification that is different from aclassification of the original input image.
 16. The computer system ofclaim 15, further comprising program instructions to generate, by theone or more processors, a report that includes a visual representationof the pertinent-negative image.
 17. The computer system of claim 15,further comprising: program instructions to create, by the one or moreprocessors, a pertinent-positive image that is a modified version of theoriginal input image and that includes fewer than all superpixels of theoriginal input image while still being predicted by the deep learningclassifier model to be in the classification of the original inputimage.
 18. The computer system of claim 17, further comprising: programinstructions to compare a plurality of modified images to identify acandidate modified image that has an amount of the original input imageremaining while still being classified in the classification of theoriginal input image, wherein each of the plurality of modified imagesis a modified version of the original input image having fewer than allportions of the input image.
 19. The computer system of claim 15,wherein the program instructions to determine the pertinent-negativeimage includes program instructions to determine that thepertinent-negative image is a result with a smallest change to theoriginal input image from among other potential modifications to theoriginal input image.
 20. The computer system of claim 15, wherein theprogram instructions to determine includes program instructions toidentify that the pertinent-negative image will be classified by thedeep learning classifier model as a second classification that isdifferent from a first classification of the original input image.